The primary input signals to inertial navigation systems are provided by inertial angular sensors such as gyros that provide attitude information and by rectilinear motion sensors such as accelerometers, with the sensor signals being continuously processed to provide signals representative of the position of the vehicle or object that carries the navigation system. In this regard, displacement of the vehicle or object in a given direction basically is determined by integration of acceleration in that direction twice with respect to time.
When navigating in the vicinity of a large mass such as the earth, the signals provided by the accelerometers must be compensated or corrected for the gravitational potential of the earth. More specifically, the signal supplied by a conventional accelerometer represents both specific force asserted on the accelerometer as a result of actual acceleration of the vehicle or object carrying the navigation system and, in addition, specific force asserted on the accelerometer as a result of the earth's gravitational field. Thus, when the vehicle or object carrying the accelerometer is freely falling under the force of gravity, the acceleration of the vehicle is purely gravitational and an accelerometer that includes no compensation or bias to offset the force of gravity supplies no output signal. Conversely, an unbiased accelerometer that is held stationary with its sensitive axis pointing toward the center mass of the earth provides a signal having a magnitude that represents gravitational acceleration at the location of the accelerometer and a sign (e.g., polarity) that indicates that the measured gravitational acceleration is away from the center of the earth. Accordingly, unless a navigation system includes appropriate correction for gravitational field, a system utilizing an unbiased accelerometer will provide a false indication that the vehicle or body carrying the system is accelerating upwardly. Since the gravitational field of the earth (and other large masses that affect the navigation process) is not uniform, simply biasing or correcting accelerometer signals for a single value of gravity will not suffice, except in the least demanding situations.
Considerable effort has been expended both with respect to theoretical analysis and emperical observation with regard to accurately determining gravitational field at and above the surface of the earth. Based on the information made available by these efforts, signal processing techniques have been developed and implemented in inertial guidance systems that operate above the surface of the earth to accurately account for gravitation effect. However, these techniques do not apply to inertial navigation systems that are utilized below the surface of the earth. One example of such a system is the type of borehole survey system that utilizes strapdown inertial guidance techniques to determine the course of a borehole (e.g., oil well) as a tool or probe that contains gyros and accelerometers is continuously moved along the borehole by a support cable.
In such a borehole survey system, continuous movement of the probe precludes accelerometer signal correction based on in situ measurement of gravitational acceleration that is made during the surveying operation. On the other hand, although the acceleration signals provided by the survey probe can be corrected for gravitational acceleration at the well head (surface of the earth), this simple form of correction often is not sufficient. Specifically, such correction does not account for variation in gravitational acceleration as a function of probe depth nor does it account for changes in gravitational acceleration that result from density differences between the stratified layers of earth and rock that are typically encountered as the probe passes along the borehole (earth mass anomalies).
Modern borehole practice, including the drilling of very deep, small diameter deviated oil wells has created an ever increasing need for more compact and precise borehole survey systems. One aspect of fulfilling this need is the requirement for a signal processing arrangement that is operable within a borehole survey system (and other types of subterranean inertial navigation systems) to provide gravity compensation that is based on depth related gravitational field gradients and, in many situations, gradients caused by density variations in the geological formation that is penetrated by the borehole.